Embedded Surfaces and Almost Complex Structures
نویسنده
چکیده
In this paper, we prove necessary and sufficient conditions for a smooth surface in a smooth 4-manifold X to be pseudoholomorphic with respect to an almost complex structure on X. In particular, this provides a systematic approach to the construction of pseudoholomorphic curves that do not minimize the genus in their homology class.
منابع مشابه
Immersions of Surfaces in Almost–complex 4–manifolds
In this note, we investigate the relation between double points and complex points of immersed surfaces in almost–complex 4–manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number of double points and the number of complex points of an immersion. We also provide a generalization of a classical genus estimate due to V.A. Rokhlin to the ...
متن کاملOn symplectic 4-manifolds and contact 5-manifolds
In this thesis we prove some results on symplectic structures on 4-dimensional manifolds and contact structures on 5-dimensional manifolds. We begin by discussing the relation between holomorphic and symplectic minimality for Kähler surfaces and the irreducibility of minimal simply-connected symplectic 4-manifolds under connected sum. We also prove a result on the conformal systoles of symplect...
متن کاملSYMPLECTIC SURFACES AND GENERIC j-HOLOMORPHIC STRUCTURES ON 4-MANIFOLDS
It is a well known fact that every embedded symplectic surface Σ in a symplectic four-manifold (X4, ω) can be made J-holomorphic for some almost-complex structure J compatible with ω. In this paper we investigate when such a structure J can be chosen generically in the sense of Taubes. The main result is stated in Theorem 1.2. As an application of this result we give examples of smooth and non-...
متن کاملFabrication of complex metallic nanostructures by nanoskiving.
This paper describes the use of nanoskiving to fabricate complex metallic nanostructures by sectioning polymer slabs containing small, embedded metal structures. This method begins with the deposition of thin metallic films on an epoxy substrate by e-beam evaporation or sputtering. After embedding the thin metallic film in an epoxy matrix, sectioning (in a plane perpendicular or parallel to the...
متن کاملSymplectomorphism Groups and Almost Complex Structures
This paper studies groups of symplectomorphisms of ruled surfaces M for symplectic forms with varying cohomology class. This cohomology class is characterised by the ratio μ of the size of the base to that of the fiber. By considering appropriate spaces of almost complex structures, we investigate how the topological type of these groups changes as μ increases. If the base is a sphere, this cha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998